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hamiltonian.cxx
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hamiltonian.cxx
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/*
This code is part of DIETA
Authored by Kirill Alpin
*/
#include <iostream>
#include <fstream>
#include <bitset>
#include "hamiltonian.h"
/*
* precalculate binomial coefficients
*/
int binomialCoeff_c(int n, int k)
{
if(k > n)
return 0;
int res = 1;
// Since C(n, k) = C(n, n-k)
if ( k > n - k )
k = n - k;
// Calculate value of [n * (n-1) *---* (n-k+1)] / [k * (k-1) *----* 1]
for (int i = 0; i < k; ++i)
{
res *= (n - i);
res /= (i + 1);
}
return res;
}
/*
* used in calculating occupation numbers
*/
int hibit(unsigned int n) {
n |= (n >> 1);
n |= (n >> 2);
n |= (n >> 4);
n |= (n >> 8);
n |= (n >> 16);
return ((n - (n >> 1)) << 1) - 1;
}
/*
* used in calculating occupation numbers
*/
static inline uint32_t log2(const int xp) {
uint32_t x = (uint32_t)xp;
uint32_t y;
asm ( "\tbsr %1, %0\n"
: "=r"(y)
: "r" (x)
);
return y+1;
}
/*
* get precalculated binomial coefficients
*/
unsigned int binomialCoeff(int m, int n, unsigned int* precalc, int particle_number)
{
return precalc[n + m * (particle_number + 2)];
}
/*
* initialize Hamiltonian
*/
Hamiltonian::Hamiltonian(std::string graph_filename, std::string params_filename) : graph(graph_filename, params_filename)
{
//initialize variables
binom_coeff = 0;
occup_list = 0;
occup_list_part = 0;
occup_list_hole = 0;
occup_lists = 0;
dims = 0;
ph_transform = graph.ph_transform;
//get number of sites
numsites = graph.site_pos.size();
//set vectors to zero
densities = VectorXd::Zero(numsites);
h_densities = VectorXd::Zero(numsites);
current_densities = MatrixXcd::Zero(numsites, numsites);
h_current_densities = MatrixXcd::Zero(numsites, numsites);
anom_current_densities = MatrixXcd::Zero(numsites, numsites);
single_operator_densities = VectorXcd::Zero(numsites);
single_operator_densities_set = false;
std::cout << "Number of sites:\t" << numsites << std::endl;
space_dims = graph.translations.size();
//get Hilbert space trunctation parameters
particle_number = graph.particle_number;
is_particle_conserving = graph.is_particle_conserving;
is_parity_conserving = graph.is_parity_conserving;
hardcore = graph.hardcore_current;
//bath site stuff
if(graph.num_bath > 0)
std::cout << "Number of bath sites:\t" << graph.num_bath << std::endl;
bath_mu = VectorXd::Zero(graph.num_bath);
bath_hopping = MatrixXcd::Zero(numsites, graph.num_bath);
//set meanfields using the parameters in the params file
for(int i = 0; i < graph.param_names.size(); ++i)
{
//set particle density mean field parameters <n>
if(graph.param_names[i][0] == 'd')
{
std::string sub = graph.param_names[i].substr(1);
int site = std::stoi(sub);
if(site < numsites)
{
densities[site] = std::real(graph.params[i]);
}
}
//set single operator expectation values
if(graph.param_names[i][0] == 'f')
{
std::string sub = graph.param_names[i].substr(1);
int site = std::stoi(sub);
if(site < numsites)
{
single_operator_densities[site] = graph.params[i];
single_operator_densities_set = true;
}
}
if(graph.param_names[i][0] == 'm')
{
if(graph.param_names[i][1] == 'a' && std::isdigit(graph.param_names[i][2]))
{
//set <a_i a_j> mean field parameters
//anom current densities
std::string sub = graph.param_names[i].substr(2);
std::string delimiter = "_";
int siteA = std::stoi(sub.substr(0, sub.find(delimiter)));
sub.erase(0, sub.find(delimiter) + delimiter.length());
int siteB = std::stoi(sub.substr(0, sub.find(delimiter)));
if(siteA < numsites && siteB < numsites)
{
anom_current_densities(siteA, siteB) = graph.params[i];
anom_current_densities(siteB, siteA) = std::conj(graph.params[i]);
current_set = true;
}
}
else if(std::isdigit(graph.param_names[i][1]))
{
//set <a^dag_i a_j> mean field parameters
//current densities
std::string sub = graph.param_names[i].substr(1);
std::string delimiter = "_";
int siteA = std::stoi(sub.substr(0, sub.find(delimiter)));
sub.erase(0, sub.find(delimiter) + delimiter.length());
int siteB = std::stoi(sub.substr(0, sub.find(delimiter)));
if(siteA < numsites && siteB < numsites)
{
current_densities(siteA, siteB) = graph.params[i];
current_densities(siteB, siteA) = std::conj(graph.params[i]);
current_set = true;
}
}
}
if(graph.param_names[i][0] == 'b')
{
//set bath site parameters
if(graph.param_names[i][1] == 'm' && std::isdigit(graph.param_names[i][2]))
{
//set bath site chemical potential
std::string sub = graph.param_names[i].substr(2);
int site = std::stoi(sub);
if(site < graph.num_bath)
bath_mu[site] = std::real(graph.params[i]);
}
else if(std::isdigit(graph.param_names[i][1]))
{
//set bath site hybridization
std::string sub = graph.param_names[i].substr(1);
std::string delimiter = "_";
int siteA = std::stoi(sub.substr(0, sub.find(delimiter)));
sub.erase(0, sub.find(delimiter) + delimiter.length());
int siteB = std::stoi(sub.substr(0, sub.find(delimiter)));
if(siteA < numsites && siteB < graph.num_bath)
bath_hopping(siteA, siteB) = graph.params[i];
}
}
}
//make parameters particle hole symmetric
h_densities = densities;
h_current_densities = current_densities;
if(numsites*(graph.max_particle == 1 ? 1 : (graph.max_particle < 4 ? 2 : log2(graph.max_particle))) > sizeof(unsigned int)*8)
{
std::stringstream ss;
ss << "Number of sites exceeds the occupation number representation size.";
throw std::invalid_argument(ss.str());
}
if(is_parity_conserving)
{
//set up Hilbert space trunctation based on parity conservation
//due to parity symmetry, the groundstate particle number defaults to numsites/2
particle_number = numsites / 2;
if(graph.max_particle != 1)
{
std::stringstream ss;
ss << "Particle number conservation not implemented for " << graph.max_particle << " particles per site.";
throw std::invalid_argument(ss.str());
}
//precalculate binomial coefficients
binom_coeff = new unsigned int[(numsites+1)*(numsites+1)];
for(int m = 0; m < numsites + 1; ++m)
for(int n = 0; n < numsites + 1; ++n)
binom_coeff[n + m * (numsites + 1)] = binomialCoeff_c(m, n);
//precalculate the occupation list
occup_lists = new unsigned int*[numsites+1];
dims = new unsigned int[numsites+1];
for(int i = 0; i < numsites+1; ++i)
{
dims[i] = binomialCoeff_c(numsites, i);
compute_occup_lookup_table(occup_lists[i], i, dims[i]);
}
//calculate the Hilbert dimension of the subsectors
unsigned int dim_even = 0;
unsigned int dim_odd = 0;
for(int i = 0; i < numsites+1; i+=2)
dim_even += dims[i];
for(int i = 1; i < numsites+1; i+=2)
dim_odd += dims[i];
if(numsites % 2 == 0)
{
dim = dim_even;
dim_part = dim_odd;
dim_hole = dim_odd;
}
else
{
dim = dim_odd;
dim_part = dim_even;
dim_hole = dim_even;
}
}
else if(is_particle_conserving)
{
//set up Hilbert space trunctation based on particle number conservation
if(graph.max_particle != 1)
{
std::stringstream ss;
ss << "Particle number conservation not implemented for " << graph.max_particle << " particles per site.";
throw std::invalid_argument(ss.str());
}
//precompute binomial coefficients
binom_coeff = new unsigned int[(numsites+1)*(particle_number+2)];
for(int m = 0; m < numsites + 1; ++m)
for(int n = 0; n < particle_number + 2; ++n)
binom_coeff[n + m * (particle_number + 2)] = binomialCoeff_c(m, n);
std::cout << "Number of particles:\t" << particle_number << std::endl;
//set dimensions
dim = binomialCoeff_c(numsites, particle_number);
dim_part = particle_number + 1 > numsites ? 1 : binomialCoeff_c(numsites, particle_number + 1);
dim_hole = particle_number - 1 < 0 ? 1 : binomialCoeff_c(numsites, particle_number - 1);
//precompute occupation numbers for N, N+1 and N-1 particle sector
compute_occup_lookup_table(occup_list, particle_number, dim);
compute_occup_lookup_table(occup_list_part, particle_number + 1 > numsites ? numsites : particle_number + 1, dim_part);
compute_occup_lookup_table(occup_list_hole, particle_number - 1 < 0 ? 0 : particle_number - 1, dim_hole);
}
else
{
//set up dimensions for the case of no Hilbert space trunctation
dim = get_dimension();
dim_part = dim;
dim_hole = dim;
}
//check if coefficients are complex
is_complex = graph.is_complex;
//precompute sqrt coefficients for boson operators
sqrt_coeff = new FLTYPE[graph.max_particle+1];
for(int i = 0; i < graph.max_particle+1; ++i)
sqrt_coeff[i] = std::sqrt((FLTYPE)i);
}
Hamiltonian::~Hamiltonian()
{
//deallocate all stuff
if(binom_coeff != 0)
{
delete[] binom_coeff;
binom_coeff = 0;
}
if(occup_list != 0)
{
delete[] occup_list;
occup_list = 0;
}
if(occup_list_hole != 0)
{
delete[] occup_list_hole;
occup_list_hole = 0;
}
if(occup_list_part != 0)
{
delete[] occup_list_part;
occup_list_part = 0;
}
if(occup_lists != 0)
{
for(int i = 0; i < numsites; ++i)
delete[] occup_lists[i];
delete[] occup_lists;
occup_lists = 0;
}
if(dims != 0)
{
delete[] dims;
dims = 0;
}
if(sqrt_coeff != 0)
{
delete[] sqrt_coeff;
sqrt_coeff = 0;
}
}
/*
* precomputes the occupation lookup table in case of Hilbert space trunctation
*/
void Hamiltonian::compute_occup_lookup_table(unsigned int* &occup_lookup, unsigned int particle_number_now, unsigned int dim_now)
{
std::vector<unsigned int> now_occup;
for(int m = 0; m < numsites - particle_number_now; ++m)
now_occup.push_back(0);
for(int n = 0; n < particle_number_now; ++n)
now_occup.push_back(1);
std::sort(now_occup.begin(), now_occup.end());
occup_lookup = new unsigned int[dim_now];
for(int i = 0; i < dim_now; ++i)
{
occup_lookup[i] = 0;
for(int j = 0; j < now_occup.size(); ++j)
occup_lookup[i] |= now_occup[j] << j;
std::next_permutation(now_occup.begin(), now_occup.end());
}
}
/*
* returns the total Hibert space dimension
*/
unsigned int Hamiltonian::get_dimension()
{
if(graph.max_particle == 1)
return 1 << numsites;
else
{
unsigned int ret = 1;
for(int i = 0; i < numsites; ++i)
ret *= graph.max_particle + 1;
return ret;
}
}
/*
* converts an occupation number vector (occup) to the Fock state index in the state vector
*/
unsigned int Hamiltonian::occup_to_index(unsigned int occup)
{
if(is_parity_conserving)
{
int ret = 0;
std::bitset<sizeof(unsigned int)*8> bito(occup);
int remaining_particles = bito.count();
int remaining_sites = numsites;
for(int i = remaining_particles % 2; i < remaining_particles; i+=2)
ret += dims[i];
for(int i = 0; i < numsites - 1; ++i)
{
int action_i = (occup >> i) & 1;
if(action_i == 1)
{
remaining_sites--;
ret += binomialCoeff(remaining_sites, remaining_particles, binom_coeff, numsites - 1);
remaining_particles--;
}
else
remaining_sites--;
}
return ret;
}
else if(is_particle_conserving)
{
int ret = 0;
int remaining_particles = current_particle_space;
int remaining_sites = numsites;
for(int i = 0; i < numsites - 1; ++i)
{
int action_i = (occup >> i) & 1;
if(action_i == 1)
{
remaining_sites--;
ret += binomialCoeff(remaining_sites, remaining_particles, binom_coeff, particle_number);
remaining_particles--;
}
else
remaining_sites--;
}
return ret;
}
else
{
if(graph.max_particle == 1)
return occup;
else
{
unsigned int ret = 0;
unsigned int base = 1;
for(int i = 0; i < numsites; ++i)
{
if(graph.max_particle < 4)
{
unsigned int soccup = (occup >> (i*2)) & 3;
ret += soccup * base;
base *= graph.max_particle + 1;
}
else
{
unsigned int soccup = (occup >> (i*log2(graph.max_particle))) & hibit(graph.max_particle);
ret += soccup * base;
base *= graph.max_particle + 1;
}
}
return ret;
}
}
}
/*
* converts a Fock state index to a occupation number vector (stored in one unsigned int)
*/
unsigned int Hamiltonian::index_to_occup(unsigned int index)
{
unsigned int occup;
if(is_parity_conserving)
{
unsigned int d = 0;
for(int i = current_particle_space % 2; i < numsites + 1; i+=2)
{
if(d <= index && d + dims[i] > index)
{
occup = occup_lists[i][index - d];
break;
}
else
d += dims[i];
}
}
else if(is_particle_conserving)
{
if(current_particle_space == particle_number)
occup = occup_list[index];
else if(current_particle_space == particle_number + 1)
occup = occup_list_part[index];
else
occup = occup_list_hole[index];
}
else
{
if(graph.max_particle == 1)
occup = index;
else
{
unsigned int ret = 0;
unsigned int work = index;
for(int i = 0; i < numsites; ++i)
{
if(graph.max_particle < 4)
{
ret |= (work % (graph.max_particle + 1)) << (i*2);
work = work / (graph.max_particle + 1);
}
else
{
ret |= (work % (graph.max_particle + 1)) << (i*log2(graph.max_particle));
work = work / (graph.max_particle + 1);
}
}
occup = ret;
}
}
return occup;
}
/*
* returns the occupation number at site index (site) given a occupation number vector (occup)
*/
unsigned int Hamiltonian::get_occup(unsigned int occup, unsigned int site)
{
if(graph.max_particle == 1)
return (occup >> site) & 1;
else
if(graph.max_particle < 4)
return (occup >> (site*2)) & 3;
else
return (occup >> (site*log2(graph.max_particle))) & hibit(graph.max_particle);
}
/*
* computes a^dag_site a_site|occup>. it is possible to use an automatic Holstein Primakoff expansion for bosons
*/
FLTYPE Hamiltonian::n_operator(unsigned int occup, unsigned int site)
{
if(ph_transform)
occup = ~occup;
if(graph.max_particle == 1)
return (FLTYPE)((occup >> site) & 1);
else
{
if(graph.max_particle < 4)
{
FLTYPE sq_n = holprim_expansion(((occup >> (site*2)) & 3) - 1);
return (FLTYPE)((occup >> (site*2)) & 3) * sq_n * sq_n;
}
else
{
FLTYPE sq_n = holprim_expansion(((occup >> (site*log2(graph.max_particle))) & hibit(graph.max_particle)) - 1);
return (FLTYPE)((occup >> (site*log2(graph.max_particle))) & hibit(graph.max_particle)) * sq_n * sq_n;
}
}
}
/*
* get Holstein Primakoff expansion of n. essentially equivalent to a taylor series of sqrt(1-n)
*/
FLTYPE Hamiltonian::holprim_expansion(int n)
{
FLTYPE ret = 1.0;
int np = n;
for(int i = 0; i < MAX_HOLPRIM_ORDER; ++i)
{
ret -= (FLTYPE)np * HOLPRIM_COEFF[i];
np *= n;
}
return ret;
}
/*
* adds a particle to the occupation number vector (occup) at site (site). if successful, returns true.
* if not, this means the site is already fully occupied.
* (coeff) returns a possible coefficient applied onto the state, like the phase due to normal ordering of fermions
* or sqrt coefficient for bosons
*/
bool Hamiltonian::add_particle(unsigned int &occup, unsigned int site, FLTYPE& coeff)
{
if(graph.particleType == ParticleType::FERMION)
{
//compute normal ordering phase factor of fermions
int rr = 0;
for(int i = 0; i < site; ++i)
rr += get_occup(occup, i);
coeff *= (1 - ((rr & 1) * 2));
}
//apply possible particle hole transfromation
if(ph_transform)
occup = ~occup;
//check if site is already fully occupied
if(get_occup(occup, site) == graph.max_particle)
return false;
//check if maximal allowed particle number is 1. indicating either fermions or hardcore bosons
if(graph.max_particle == 1)
{
//add particle at site (site)
occup = occup | (1 << site);
//reverse particle hole transfromation
if(ph_transform)
occup = ~occup;
return true;
}
else
{
if(graph.max_particle < 4)
{
//calculate sqrt coefficient for bosons. automatic Holstein Primakoff expansion is also possible
coeff *= sqrt_coeff[((occup >> (site*2))&3) + 1] * holprim_expansion((occup >> (site*2))&3);
//apply bit magic to add particle
occup = (((occup)&(~(3<<(site*2))))) | ((((occup >> (site*2))&3) + 1) << (site*2));
//reverse particle hole transfromation
if(ph_transform)
occup = ~occup;
return true;
}
else
{
//calculate sqrt coefficient for bosons. automatic Holstein Primakoff expansion is also possible
coeff *= sqrt_coeff[((occup >> (site*log2(graph.max_particle)))&hibit(graph.max_particle)) + 1] * holprim_expansion((occup >> (site*log2(graph.max_particle)))&hibit(graph.max_particle));
//apply more bit magic to add particle
occup = (((occup)&(~(hibit(graph.max_particle)<<(site*log2(graph.max_particle)))))) | ((((occup >> (site*log2(graph.max_particle)))&hibit(graph.max_particle)) + 1) << (site*log2(graph.max_particle)));
//reverse particle hole transfromation
if(ph_transform)
occup = ~occup;
return true;
}
}
}
/*
* equivalent to add_particle, only that here a particle is removed from (occup)
*/
bool Hamiltonian::remove_particle(unsigned int &occup, unsigned int site, FLTYPE& coeff)
{
if(graph.particleType == ParticleType::FERMION)
{
//compute normal ordering phase factor of fermions
int rr = 0;
for(int i = 0; i < site; ++i)
rr += get_occup(occup, i);
coeff *= (1 - ((rr & 1) * 2));
}
//apply possible particle hole transfromation
if(ph_transform)
occup = ~occup;
//check if site is already at zero occupation
if(get_occup(occup, site) == 0)
return false;
//check if maximal allowed particle number is 1. indicating either fermions or hardcore bosons
if(graph.max_particle == 1)
{
//remove particle at site (site)
occup = occup & (~(1 << site));
//reverse particle hole transfromation
if(ph_transform)
occup = ~occup;
return true;
}
else
{
if(graph.max_particle < 4)
{
//calculate sqrt coefficient for bosons. automatic Holstein Primakoff expansion is also possible
coeff *= sqrt_coeff[((occup >> (site*2))&3)] * holprim_expansion(((occup >> (site*2))&3) - 1);
//apply bit magic to remove particle
occup = (((occup)&(~(3<<(site*2))))) | ((((occup >> (site*2))&3) - 1) << (site*2));
//reverse particle hole transfromation
if(ph_transform)
occup = ~occup;
return true;
}
else
{
//calculate sqrt coefficient for bosons. automatic Holstein Primakoff expansion is also possible
coeff *= sqrt_coeff[((occup >> (site*log2(graph.max_particle)))&hibit(graph.max_particle))] * holprim_expansion(((occup >> (site*log2(graph.max_particle)))&hibit(graph.max_particle)) - 1);
//apply more bit magic to remove particle
occup = (((occup)&(~(hibit(graph.max_particle)<<(site*log2(graph.max_particle)))))) | ((((occup >> (site*log2(graph.max_particle)))&hibit(graph.max_particle)) - 1) << (site*log2(graph.max_particle)));
//reverse particle hole transfromation
if(ph_transform)
occup = ~occup;
return true;
}
}
}
FARRAY Hamiltonian::single_particle_state(unsigned int site)
{
//TODO legacy code. not compatible with complex hamiltonian
FARRAY ret = FARRAY::Zero(dim);
unsigned int occup = 0;
FLTYPE coeff = 1.0;
add_particle(occup, site, coeff);
ret[occup_to_index(occup)] = 1.0;
return ret;
}
/*
* check sanity of Hibert space dimension
*/
void Hamiltonian::check_hilbert_dim(unsigned int dim_now)
{
if(is_particle_conserving)
{
if(dim_now != dim_hole && dim_now != dim_part && dim_now != dim)
{
std::stringstream ss;
ss << "Invalid hilbert space dimension.";
throw std::invalid_argument(ss.str());
}
if(current_particle_space != particle_number
&& current_particle_space != particle_number + 1
&& current_particle_space != particle_number - 1)
{
std::stringstream ss;
ss << "Invalid subspace.";
throw std::invalid_argument(ss.str());
}
}
else
{
if(dim_now != dim)
{
std::stringstream ss;
ss << "Invalid hilbert space dimension.";
throw std::invalid_argument(ss.str());
}
}
}
/*
* set current particle space on which the code operates
*/
void Hamiltonian::set_particle_space(unsigned int p)
{
if(is_particle_conserving || is_parity_conserving)
current_particle_space = p;
}
/*
* returns a^dag_(site_num) a_(site_num)|s>
*/
template<typename T>
T Hamiltonian::nop_site(T s, int site_num)
{
T ret = T::Zero(s.size());
check_hilbert_dim(s.size());
if(is_particle_conserving || is_parity_conserving)
{
std::stringstream ss;
ss << "Not implemented.";
throw std::invalid_argument(ss.str());
}
for(unsigned int i = 0; i < s.size(); ++i)
{
unsigned int occup = index_to_occup(i);
auto const site = graph.site_pos[site_num];
switch(site.type)
{
case 'A': //chemical potential
{
FLTYPE site_occup = n_operator(occup, site.num);
if(ph_transform)
site_occup = 1.0 - site_occup;
ret[i] += site_occup * s[i];
}
break;
case 'F': //on site term a+adag
{
}
break;
case 'N': //noop
break;
default:
std::stringstream ss;
ss << "Site type " << site.type << " not implemented.";
throw std::invalid_argument(ss.str());
break;
}
}
return ret;
}
template VectorXd Hamiltonian::nop_site(VectorXd s, int site_num);
template VectorXcd Hamiltonian::nop_site(VectorXcd s, int site_num);
/*
* used to incorporate complex valued Hamiltonians
*/
std::complex<FLTYPE> Hamiltonian::K(std::complex<FLTYPE> val, Tag<VectorXcd>)
{
return val;
}
FLTYPE Hamiltonian::K(std::complex<FLTYPE> val, Tag<VectorXd>)
{
return val.real();
}
/*
* set fields F_field, mu_field and meanF_field given the parameters of the Hamiltonian
*/
void Hamiltonian::setFields()
{
F_field = VectorXcd::Zero(numsites);
mu_field = VectorXd::Zero(numsites);
meanF_field = VectorXcd::Zero(numsites);
for(auto const& site: graph.site_pos)
{
switch(site.type)
{
case 'A': //chemical potential
{
mu_field[site.num] += std::real(P(site.ind, Tag<VectorXcd>()));
}
break;
default:
break;
}
}
for(auto const& edge: graph.edges)
{
switch(edge.type)
{
case 'F': //a+a^dag term. edge.b is unused
{
unsigned int siteA = edge.a;
F_field[siteA] += P(edge.ind, Tag<VectorXcd>());
}
break;
default:
break;
}
}
for(auto const& edge: graph.mean_edges)
{
switch(edge.type)
{
case 'C':
{
unsigned int siteA = edge.a;
unsigned int siteB = edge.b;
mu_field[siteA] += std::real(P(edge.ind, Tag<VectorXcd>())) * densities[siteB];
mu_field[siteB] += std::real(P(edge.ind, Tag<VectorXcd>())) * densities[siteA];
}
break;
case 'D':
{
unsigned int siteA = edge.a;
unsigned int siteB = edge.b;
meanF_field[siteB] += P(edge.ind, Tag<VectorXcd>()) * densities[siteA];
}
break;
default:
break;
}
}
F_field += meanF_field;
mu_field *= -1;
}
/*
* applies the Hamiltonian onto a state by multiplication
*/
template<typename T>
T Hamiltonian::operator* (const T &s)
{
//set the returning state vector
T ret = T::Zero(s.size());
//check if vector size is compatible with the Hamiltonian
check_hilbert_dim(s.size());
if(is_particle_conserving)
{
//only a subset of operation is supported for particle number conserving Hamiltonians
//iterate over all Fock state indices to construct the returning vector
#pragma omp parallel for
for(unsigned int i = 0; i < s.size(); ++i)
{
unsigned int occup = index_to_occup(i);
//on site stuff
//iterate over all sites
for(auto const& site: graph.site_pos)
{
switch(site.type)
{
case 'A': //chemical potential
{
FLTYPE site_occup = n_operator(occup, site.num);
ret[i] += PA(site.ind) * site_occup * s[i];
}
break;
case 'N': //noop
break;
default:
std::stringstream ss;
ss << "Site type " << site.type << " not implemented or not particle number conserving.";
throw std::invalid_argument(ss.str());
break;
}
}
//inter site stuff
//iterate over all edges connecting sites inside the graph
for(auto const& edge: graph.edges)
{
switch(edge.type)
{
case 'A': //hopping term c^dag*c+c*c^dag
{
unsigned int siteA = edge.a;
unsigned int siteB = edge.b;
//forward
unsigned int occup_work = occup;
bool success = true;
FLTYPE coeff = 1.0;
success &= remove_particle(occup_work, siteA, coeff);
success &= add_particle(occup_work, siteB, coeff);
if(success)
ret[i] += (coeff * std::conj(PA(edge.ind))) * s[occup_to_index(occup_work)];
//backward
occup_work = occup;
success = true;
coeff = 1.0;
success &= add_particle(occup_work, siteA, coeff);
success &= remove_particle(occup_work, siteB, coeff);
if(success)
ret[i] += (coeff * PA(edge.ind)) * s[occup_to_index(occup_work)];
}
break;
case 'C': //interaction n_a*n_b
if(!no_interaction)
{
unsigned int siteA = edge.a;
unsigned int siteB = edge.b;
ret[i] += PA(edge.ind) * n_operator(occup, siteA) * n_operator(occup, siteB) * s[i];
}
break;
default:
std::stringstream ss;
ss << "Edge type " << edge.type << " not implemented or not particle number conserving.";
throw std::invalid_argument(ss.str());
break;
}
}
}
}
else
{
//iterate over all Fock state indices to construct the returning vector
#pragma omp parallel for
for(unsigned int i = 0; i < s.size(); ++i)
{
unsigned int occup = index_to_occup(i);
//on site stuff
//iterate over all sites
for(auto const& site: graph.site_pos)
{
switch(site.type)
{
case 'A': //chemical potential
{
FLTYPE site_occup = n_operator(occup, site.num);
ret[i] += PA(site.ind) * (FLTYPE)site_occup * s[i];
}
break;
case 'N': //noop
break;
default:
std::stringstream ss;
ss << "Site type " << site.type << " not implemented.";
throw std::invalid_argument(ss.str());
break;
}
}
//inter site stuff
//iterate over all edges connecting sites inside the graph
for(auto const& edge: graph.edges)
{
switch(edge.type)
{
case 'A': //hopping term c^dag*c+c*c^dag
{
unsigned int siteA = edge.a;
unsigned int siteB = edge.b;
//forward
unsigned int occup_work = occup;
bool success = true;
FLTYPE coeff = 1.0;
success &= remove_particle(occup_work, siteA, coeff);
success &= add_particle(occup_work, siteB, coeff);
if(success)
ret[i] += (coeff * std::conj(PA(edge.ind))) * s[occup_to_index(occup_work)];
//backward
occup_work = occup;
success = true;
coeff = 1.0;
success &= remove_particle(occup_work, siteB, coeff);
success &= add_particle(occup_work, siteA, coeff);
if(success)
ret[i] += (coeff * PA(edge.ind)) * s[occup_to_index(occup_work)];
}
break;
case 'B': //pair term c*c+c^dag*c^dag
{
unsigned int siteA = edge.a;
unsigned int siteB = edge.b;
//forward
unsigned int occup_work = occup;
bool success = true;
FLTYPE coeff = 1.0;
success &= add_particle(occup_work, siteA, coeff);
success &= add_particle(occup_work, siteB, coeff);
if(success)
ret[i] += (coeff * std::conj(PA(edge.ind))) * s[occup_to_index(occup_work)];